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Chapter 5: Q. 290 (page 672)

In the following exercises, solve each system by graphing.

2x+4y鈮�8y鈮�34x

Short Answer

Expert verified

The solution set is the region shaded with a darker color.

Step by step solution

01

Step 1. Given Information

The given system is2x+4y鈮�8y鈮�34x.

02

Step 2. Plot the first inequality

  • To plot the inequality 2x+4y鈮�8, draw the solid line 2x+4y=8because the inequality sign includes equality.
  • The point (0,0)does not satisfies the inequality, so shade the region that does not include the origin.

03

Step 3. Plot the second inequality

  • To plot the inequality y鈮�34x, draw the solid line y=34xbecause the inequality sign includes equality.
  • The point (0,0) satisfies the inequality, so shade the region that includes the origin.

  • The solution set is the region shaded with a darker color.
04

Step 4. Check the solution

  • One of the points that lie in the solution set is (8,0).
  • Check if the point satisfies the inequalities.

2(8)+4(0)鈮�?816鈮�80鈮�?34(8)0鈮�6

  • As both the inequalities are satisfied, the solution is verified.

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